XCSP 2.1 Benchmark Database

Instance: normalized-rand-2-40-40-135-650-29-ext
Number of variables: 40
Number of constraints: 135
Satisfiable: True
Timestamp: 2025-07-20 22:09:32
Stampede: v1.1.0-239-ge51ee236
Boost: 1.75.0

Component #1

Number of variables: 40
Number of constraints: 135

General features

Coarse blocks: 10,800
Value tables: 40

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Arity 2 2 2.00 2.00 270 MAX VALUE 93.57 0.00 0.00 0.00

Coarse blocks size 3 26 13.97 14.00 150,914 MAX VALUE 28,213.90 3.02 0.22 2.52

Relational linkage 0.07 0.42 0.25 0.25 407.98 0.00 -2,219.12 0.05 0.20 2.11

Tightness 0.62 0.68 0.65 0.65 87.84 0.00 -58.04 0.01 0.02 3.88

Tuples 508 610 558.94 556.00 75,457 MAX VALUE 853.94 18.91 0.03 3.88

Values 40 40 40.00 40.00 1,600 MAX VALUE 147.56 0.00 0.00 0.00

Value table constraints 3 11 6.75 6.50 270 1.20e+32 73.87 2.21 0.33 2.00

Value table partitions 40 40 40.00 40.00 1,600 MAX VALUE 147.56 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Arity	2	2	2.00	2.00	270	MAX VALUE	93.57	0.00	0.00	0.00
Coarse blocks size	3	26	13.97	14.00	150,914	MAX VALUE	28,213.90	3.02	0.22	2.52
Relational linkage	0.07	0.42	0.25	0.25	407.98	0.00	-2,219.12	0.05	0.20	2.11
Tightness	0.62	0.68	0.65	0.65	87.84	0.00	-58.04	0.01	0.02	3.88
Tuples	508	610	558.94	556.00	75,457	MAX VALUE	853.94	18.91	0.03	3.88
Values	40	40	40.00	40.00	1,600	MAX VALUE	147.56	0.00	0.00	0.00
Value table constraints	3	11	6.75	6.50	270	1.20e+32	73.87	2.21	0.33	2.00
Value table partitions	40	40	40.00	40.00	1,600	MAX VALUE	147.56	0.00	0.00	0.00

Tree decomposition

Number of clusters: 24
Number of leaves: 12
Tree depth: 5
CIR: 0.31
Independent Cluster Pairs: 78
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/Tree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/Tree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/Tree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 3 33 12.04 9.00 289 2.09e+23 53.70 8.80 0.73 2.73

Variables per cluster 4 17 8.46 7.00 203 1.19e+21 48.53 4.15 0.49 2.20

Separator constraints 0 28 6.42 4.00 154 0 None 7.65 1.19 2.31

Separator variables 0 16 6.79 6.00 163 0 None 4.01 0.59 2.25

Clusters per var 1 13 5.08 5.00 203 5.10e+21 49.98 3.68 0.72 2.11

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	3	33	12.04	9.00	289	2.09e+23	53.70	8.80	0.73	2.73
Variables per cluster	4	17	8.46	7.00	203	1.19e+21	48.53	4.15	0.49	2.20
Separator constraints	0	28	6.42	4.00	154	0	None	7.65	1.19	2.31
Separator variables	0	16	6.79	6.00	163	0	None	4.01	0.59	2.25
Clusters per var	1	13	5.08	5.00	203	5.10e+21	49.98	3.68	0.72	2.11

Dual tree decomposition

Number of clusters: 38
Number of leaves: 16
Tree depth: 6
CIR: 0.33
Independent Cluster Pairs: 223
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/DualTree1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/DualTree1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/DualTree1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Cluster constraints 13 156 59.71 58.00 2,269 MAX VALUE 147.44 36.61 0.61 3.35

Variables per cluster 7 53 19.47 16.00 740 MAX VALUE 107.11 11.47 0.59 2.96

Separator constraints 0 87 36.71 33.00 1,395 0 None 22.44 0.61 3.12

Separator variables 0 40 15.92 14.50 605 0 None 8.75 0.55 3.03

Clusters per variable 1 11 5.48 6.00 740 MAX VALUE 203.83 2.75 0.50 2.25

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Cluster constraints	13	156	59.71	58.00	2,269	MAX VALUE	147.44	36.61	0.61	3.35
Variables per cluster	7	53	19.47	16.00	740	MAX VALUE	107.11	11.47	0.59	2.96
Separator constraints	0	87	36.71	33.00	1,395	0	None	22.44	0.61	3.12
Separator variables	0	40	15.92	14.50	605	0	None	8.75	0.55	3.03
Clusters per variable	1	11	5.48	6.00	740	MAX VALUE	203.83	2.75	0.50	2.25

Primal graph

Density: 17.31%
MCB compute time (ms): 4
MCB cycles: 97
Triangles: 53
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/Primal1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/Primal1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/Primal1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.40 0.19 0.19 7.62 0.00 None 0.10 0.52 3.02

Degree 3 11 6.75 6.50 270 1.20e+32 73.87 2.21 0.33 2.00

Eccentricity None None None None None None None None None None

MCB cycle size 3 4 3.49 3.00 339 MAX VALUE 120.37 0.50 0.14 0.69

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.40	0.19	0.19	7.62	0.00	None	0.10	0.52	3.02
Degree	3	11	6.75	6.50	270	1.20e+32	73.87	2.21	0.33	2.00
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	4	3.49	3.00	339	MAX VALUE	120.37	0.50	0.14	0.69

Triangulated primal graph

Density: 38.33%
MCB compute time (ms): 4
MCB cycles: 314
Triangles: 1,345

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.58 1.00 0.81 0.76 32.35 0.00 -9.06 0.14 0.17 2.91

Degree 3 28 14.95 16.50 598 MAX VALUE 98.15 8.79 0.59 2.64

Eccentricity None None None None None None None None None None

MCB cycle size 3 3 3.00 3.00 942 MAX VALUE 344.96 0.00 0.00 0.00

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.58	1.00	0.81	0.76	32.35	0.00	-9.06	0.14	0.17	2.91
Degree	3	28	14.95	16.50	598	MAX VALUE	98.15	8.79	0.59	2.64
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	3	3.00	3.00	942	MAX VALUE	344.96	0.00	0.00	0.00

Dual graph

Density: 9.66%
MCB compute time (ms): 124
MCB cycles: 841
Triangles: None
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/Dual1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/Dual1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/Dual1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.44 0.71 0.51 0.49 68.24 0.00 -92.61 0.05 0.09 3.55

Degree 6 19 12.95 13.00 1,748 MAX VALUE 341.91 2.90 0.22 2.40

Eccentricity None None None None None None None None None None

MCB cycle size 3 5 3.19 3.00 2,680 MAX VALUE 968.52 0.42 0.13 0.51

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.44	0.71	0.51	0.49	68.24	0.00	-92.61	0.05	0.09	3.55
Degree	6	19	12.95	13.00	1,748	MAX VALUE	341.91	2.90	0.22	2.40
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	5	3.19	3.00	2,680	MAX VALUE	968.52	0.42	0.13	0.51

Minimal dual graph

Density: 2.54%
MCB compute time (ms): 33
MCB cycles: 96

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.33 0.01 0.00 1.50 0.00 None 0.05 4.90 0.21

Degree 2 5 3.41 3.00 460 MAX VALUE 163.05 0.64 0.19 0.96

Eccentricity None None None None None None None None None None

MCB cycle size 3 9 6.71 7.00 644 MAX VALUE 180.36 1.40 0.21 1.70

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.00	0.33	0.01	0.00	1.50	0.00	None	0.05	4.90	0.21
Degree	2	5	3.41	3.00	460	MAX VALUE	163.05	0.64	0.19	0.96
Eccentricity	None	None	None	None	None	None	None	None	None	None
MCB cycle size	3	9	6.71	7.00	644	MAX VALUE	180.36	1.40	0.21	1.70

Triangulated dual graph

Density: 37.21%
Triangles: 52,152

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.62 1.00 0.81 0.77 109.06 0.00 -29.99 0.11 0.13 4.33

Degree 6 89 49.87 56.00 6,732 MAX VALUE 497.06 27.51 0.55 3.89

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.62	1.00	0.81	0.77	109.06	0.00	-29.99	0.11	0.13	4.33
Degree	6	89	49.87	56.00	6,732	MAX VALUE	497.06	27.51	0.55	3.89
Eccentricity	None	None	None	None	None	None	None	None	None	None

Triangulated minimal dual graph

Density: 11.46%

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.50 1.00 0.77 0.69 104.46 0.00 -38.12 0.18 0.23 3.03

Degree 2 48 15.36 7.00 2,074 MAX VALUE 293.25 15.52 1.01 2.90

Eccentricity None None None None None None None None None None

Feature	min	max	mean	median	sum	prod	ln(prod)	std_dev	COV	ENT
Clustering coefficient	0.50	1.00	0.77	0.69	104.46	0.00	-38.12	0.18	0.23	3.03
Degree	2	48	15.36	7.00	2,074	MAX VALUE	293.25	15.52	1.01	2.90
Eccentricity	None	None	None	None	None	None	None	None	None	None

Incidence graph

Density: 1.77%
MCB compute time (ms): 24
MCB cycles: 96
Dot-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/Incidence1.dot
PDF-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/Incidence1.pdf
JSON-file path: https://consystlab.unl.edu/Visualization/graphFiles/tightness0.65/normalized-rand-2-40-40-135-650-29-ext/Incidence1.json

Feature min max mean median sum prod ln(prod) std_dev COV ENT

Clustering coefficient 0.00 0.00 0.00 0.00 0.00 0.00 None 0.00 None 0.00

Degree 2 11 3.09 2.00 540 MAX VALUE 167.44 2.26 0.73 1.00

Eccentricity None None None None None None None None None None

MCB cycle size 6 8 6.98 6.00 670 MAX VALUE 185.53 1.00 0.14 0.69

XCSP 2.1 Benchmarks